Problem Kinematics Equations

[tl8]

For those that know me, I tend to be able to create a large number of add on ideas at once. Anyway my latest add on attempt is an aircraft tug. While a basic vehicle is working I want to add a semi realistic towing motion.

Long story short, I have been able to reduce my problem in to a 'simple' model.

Basically I would like information, links or equations that can work out these 3 outputs.

Friction Force along the same vector as Force in (The magnitude of Fout)
Angle alpha and Angle beta.

As this is in Orbiter, this should be calculated over a known timestep.
All initial position/conditions should be known and point 1 should be considered as 0,0 and fixed.
The primary input will be the Force in.

Any help at all that points me in the right direction is appreciated.

 

[tl8]

Have had a bit of success. I now have the process to get what I want.

The top figure shows what I need to work out. Inverse Jacobian and Forward Dynamics. I also need to work out what the force is at the end effector (I assume that means point 3)

 

[Moach]

the easies way to "simulate" a flexible tug is by creating a full-strenght "bungee" spring between the two objects

(wait what??)


lets build this from the ground up...
we begin by connecting the two objects with a spring - a "spring" is a type of physics constraint (very common in physics engines) which applies force to bring two objects together....

a linear spring is the most basic type - it pulls the end effector with the same power towards the target regardless of the distance between them....

too basic for what we want, right?

moreover, we can have an exponential spring... the "pull" force gets stronger by the square of the distance - opposite of how gravity works

still not quite what we want... but these concepts need to be understood before we proceed...


but what if, instead of letting the spring pull all the way to the target, we cut off the "pull" once the end effector gets close enough... now we have an radius around the target where there will be no force applied to the other end...

this is called a "bungee" spring - since it behaves just like a bungee-jumping cord - note how jumpers will free-fall untill the length of the cord is reached - only then it begins to stretch and pull the thrill-seeking fellow back up


but this is still too "elastic" for our needs, right?

so let's have the spring apply full power right away once the two objects come apart further than the set range - aha, a rope!



hope this helps...

 

[tl8]

No it doesn't. Mainly because I know the model I want, I just need to implement it.

Also Orbiter is not really designed for this and hence does not have some of the tool required. So using your model would put me in the exact same place as I am now.

FWIIW this really is only for visuals. The actual movement of the tug will be handled by Orbiter... (Think ground based RMS)

 

[Moach]

aaah, i see - for some reason i was thinking "tug" as in "tow", like a sailplane...

you mean a "tug" tug - like those tractors that push the aircraft from the gates


yes, i think you are correct in that Orbiter does not have the tools to properly accomodate this type of mechanic... it's gonna be some "manual" labour to pull this off...

assuming a tug has only a single movable joint, you don't have to go as far as inverse kinematics, i think...

but you lost me in "only for visuals"... how is Orbiter supposed to handle the "tugging" action? - or is one supposed to drive the ship while the tug "acts" like it's pulling? (a clever idea, actually)

 

[tl8]

As the little chart above, no inverse kinematics, just inverse jacobian and forward dynamics.

As for the single joint, the model in the first post. The bar between the tow vehicle and the plane is link 1-2, the plane itself is link 2-3.

As for what I want, the tug is a parent attachment to the child (plane) as such the plane has no effect on the tug. I will add a few things to the tug model so that Orbiter can simulate that relationship.

What I am after is a set of equations so that I can make the attachment point move. Like an RMS in space basically.

As I said before all I need is to work out the inverse jacobian and forward dynamics of the links.

 

[tl8]

Robot Manipulator Equations

For those from the future, here is the overall algorithm that will be used. As far as I know any type 1 manipulator can be represented with this algorithm.

The equations that need to be done are
Step 1
Step 2 a,b,c,d,e
Step 4 b
Step 5,6,7

Big thanks needs to go to Urwumpe who helped develop the the algorithm and fixing errors